Nucleon Generalized Parton Distributions Research Articles

Erratum to: Chiral perturbation theory for nucleon generalized parton distributions

Erratum to: Chiral perturbation theory for nucleon generalized parton distributions

Moments of nucleon generalized parton distributions from lattice QCD simulations at physical pion mass

We present results for the moments of nucleon isovector vector and axial generalised parton distribution functions computed within lattice QCD. Three ensembles of maximally twisted mass clover-improved fermions simulated with a physical value of the pion mass are analyzed. Two of these ensembles are generated using two degenerate light quarks. A third ensemble is used having, in addition to the light quarks, strange and charm quarks in the sea. A careful analysis of the convergence to the ground state is carried out that is shown to be essential for extracting the correct nucleon matrix elements. This allows a controlled determination of the unpolarised, helicity and tensor second Mellin moments. The vector and axial-vector generalised form factors are also computed as a function of the momentum transfer square up to about 1 GeV$^2$. The three ensembles allow us to check for unquenching effects and to assess lattice finite volume effects.

Gravitational form factors and angular momentum densities in light-front quark-diquark model

We investigate the gravitational form factors (GFFs) and the longitudinal momentum densities ($p^+$ densities) for proton in a light-front quark-diquark model. The light-front wave functions are constructed from the soft-wall AdS/QCD prediction. The contributions from both the scalar and the axial vector diquarks are considered here. The results are compared with the consequences of a parametrization of nucleon generalized parton distributions (GPDs) in the light of recent MRST measurements of parton distribution functions (PDFs) and a soft-wall AdS/QCD model. The spatial distribution of angular momentum for up and down quarks inside the nucleon has been presented. At the density level, we illustrate different definitions of angular momentum explicitly for an up and down quark in the light-front quark-diquark model inspired by AdS/QCD.

Momentum transfer dependence of generalized parton distributions

We revisit the model for parametrization of momentum dependence of nucleon generalized parton distributions in the light of recent MRST measurements of parton distribution functions. Our parametrization method with minimum set of free parameters give a sufficiently good description of data for Dirac and Pauli electromagnetic form factors of proton and neutron at small and intermediate values of momentum transfer. We also calculate the GPDs for up and down quark by decomposing the electromagnetic form factors for nucleon using the charge and isospin symmetry and also study the evolution of GPDs to a higher scale. We further investigate the transverse charge densities for both the unpolarized and transversely polarized nucleon and compare our results with the Kelly's distribution.

Light-front representation of chiral dynamics with Δ isobar and large-N c relations

Transverse densities describe the spatial distribution of electromagnetic current in the nucleon at fixed light-front time. At peripheral distances b = O(M_pi^{-1}) the densities are governed by chiral dynamics and can be calculated model-independently using chiral effective field theory (EFT). Recent work has shown that the EFT results can be represented in first-quantized form, as overlap integrals of chiral light-front wave functions describing the transition of the nucleon to soft-pion-nucleon intermediate states, resulting in a quantum-mechanical picture of the peripheral transverse densities. We now extend this representation to include intermediate states with Delta isobars and implement relations based on the large-N_c limit of QCD. We derive the wave function overlap formulas for the Delta contributions to the peripheral transverse densities by way of a three-dimensional reduction of relativistic chiral EFT expressions. Our procedure effectively maintains rotational invariance and avoids the ambiguities with higher-spin particles in the light-front time-ordered approach. We study the interplay of pi-N and pi-Delta intermediate states in the quantum-mechanical picture of the densities in a transversely polarized nucleon. We show that the correct N_c-scaling of the charge and magnetization densities emerges as the result of the particular combination of currents generated by intermediate states with degenerate N and Delta. The off-shell behavior of the chiral EFT is summarized in contact terms and can be studied easily. The methods developed here can be applied to other peripheral densities and to moments of the nucleon's generalized parton distributions.

Nucleon-generalized parton distributions in the light-front quark model

We incorporate the perturbative evolution effects in the generalized parton distributions (GPDs) calculated in effective light-front quark model for the nucleon. The perturbative effects enters into formalism through the evolution of GPDs according to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-like (DGLAP) equation. We obtain the evolved GPDs in the momentum space and transverse impact parameter space. We observe that combining the light front quark model with the perturbative evolution effects, give the effective model for studying the phenomenological GPDs

Generalized Parton Distributions for Nucleon in the Impact Parameter Space

We investigate the generalized parton distributions (GPDs) for the proton and neutron in both momentum and position space in the soft-wall approach of anti-de Sitter/QCD model. The soft-wall model is based upon an action which incorporates confinement through the presence of a background dilaton field and the contribution of higher Fock states are holographically incorporated via studying the dynamics of 5D fermion fields of different scaling dimension. Our results are comparable with the other phenomenological models of the nucleon GPDs.

LIGHT-CONE 2014: Theory and Experiment for Hadrons on the Light-Front

The 2014 edition of the Light-Cone meeting took place at the North Carolina State University (NCSU) in Raleigh, North Carolina on 26–30 May http://www.physics.ncsu.edu/LC2014/). The local organizing committee consisted of myself as the chair of the committee, J. Blondin (NCSU), H. Gao (Duke), D. Lee (NCSU), W. Melnitchouk (Jefferson Lab), T. Schaefer (NCSU), M. Unsal (NCSU), with L. Cochran and R. Bennett providing administrative support. This series of meetings is held under the auspices of the International Light Cone Advisory Committee (ILCAC), Inc. (http://www.ilcacinc.org). The Workshop was supported in part by generous contributions from Jefferson Lab, the College of Sciences at NCSU, and the NCSU Department of Physics. In particular, the support from NCSU allowed ILCAC to award this year’s McCartor Fellowships to four young physicists, enabling them to attend the conference and present the results of their research. LIGHT-CONE 2014 had over 70 participants, who presented a total of 65 talks and 4 posters. An emphasis on the interface between theory and experiment in hadron physics was a feature of this year’s meeting, with several experimental talks from Jefferson Lab (R. McKeown, L. Elouadrhiri) and COMPASS at CERN (A. Ferrero, I. Choi), discussing recent results and future perspectives of hadron physics at their facilities. The workshop covered many topics in hadron phenomenology related to the 12 GeV upgrade at Jefferson Lab, including nucleon generalized parton distributions (GPDs) (F. Wang, Y. Zhao, S. Liuti) and deeplyvirtual Compton scattering (B. Pasquini), Compton form factors (B. Bakker), transverse momentum dependent distributions (TMDs) (D. Boer, A. Metz), and parton distribution functions (P. Jimenez-Delgado). There was discussion of flavor asymmetries in the nucleon sea (J.-C. Peng, W. Melnitchouk), the deuteron b1 structure function (G.Miller), the 3He spectral function (S. Scopetta) and the pion distribution amplitude (A.Radyushkin, N. Stefanis). A variety of other, more formal theoretical topics in QCD and QED were also presented, including chiral symmetry breaking and confinement (P. Hoyer, I. Cloet, M. Schindler), Bethe-Salpeter and Dyson-Schwinger equations (P. Tandy, A. Bashir, M. Viviani, V. Karmanov), light-front models (G. Salme, T. Pena, H. Choi), and issues involving bound states and zero-modes (W. Polyzou, T. Frederico, A. Ilderton). Recent progress in light-front holography and AdS/QCD (R. Sandapen), as well as computational developments in many-body dynamics (J. Vary) were also highlighted. Some particularly stimulating presentations were on issues related to the proton spin (C. Lorce), the proton charge radius (S. Glazek), GPDs and TMDs, as well as light-front chiral sum rules (S. Beane). The closing presentation was given by S. Brodsky. A half-day excursion wasmade to several local museums (Art, History, Natural Sciences) andwas followed by theWorkshop dinner. During the dinner proceedings, as the Chair of LC2014 and ILCAC, I had the privilege to present awards to the four McCartor Fellowship recipients: Tim Hobbs (Indiana University), Yang Li (Iowa

Generalized parton distributions in the soft-wall model of AdS/QCD

We present a numerical analysis of helicity independent nucleon generalized parton distributions (GPDs) using the known formalism based on inclusion of higher Fock states in the soft-wall approach of the anti-de Sitter/QCD model. We calculate the momentum space GPDs by matching the electromagnetic form factors in the AdS model to the sum rules in QCD. We investigate their Mellin moments, transverse impact parameter GPDs, transverse mean square radius, and transverse width. We further extend this work to investigate the charge and anomalous magnetization densities for both unpolarized and transversely polarized nucleons. A comparison of results on density functions with phenomenological parametrization is also presented.

First moments of nucleon generalized parton distributions in chiral perturbation theory at full one-loop order

In this paper we present chiral extrapolation formulas for the generalized form factors connected to the first moments of chiral-even generalized parton distributions. For the description of QCD at low energies we employ the framework of two-flavor covariant baryon chiral perturbation theory at full one-loop accuracy. Our results are well suited for the extrapolation of lattice QCD data to physical quark masses.

NEW MODEL FOR NUCLEON GENERALIZED PARTON DISTRIBUTIONS

We describe a new type of models for nucleon generalized parton distributions (GPDs) H and E. They are heavily based on the fact nucleon GPDs require to use two forms of double distribution (DD) representations. The outcome of the new treatment is that the usual "DD+D-term" construction should be amended by an extra term, [Formula: see text] which has the DD structure α/βe(β, α), with e(β, α) being the DD that generates GPD E(x, ξ). We found that this function, unlike the D-term, has support in the whole -1 ≤ x ≤ 1 region. Furthermore, it does not vanish at the border points |x| = ξ.

Sum rules for nucleon generalized parton distributions and border function formulation

The newy developed approach to model nucleon generalized parton distributions (GPDs) H and E$ is based on two types of their representation in terms of double distributions. Within this approach, we re-consider the derivation of GPD sum rules that allow to use border functions H(x,x) and E(x,x) instead of full GPDs H(x,\xi) and E(x,\xi) in the integrals producing Compton form factors of deeply virtual Compton scattering. Using factorized DD Ansatz to model GPDs, we discuss the relation between the border functions and underlying parton densities. We find that a substantial contribution to H(x,x) border function comes from the extra term required by new DD representations and related to E(x,\xi) GPD.

Nucleon form factors and moments of generalized parton distributions usingNf=2+1+1twisted mass fermions

We present results on the axial and the electromagnetic form factors of the nucleon, as well as, on the first moments of the nucleon generalized parton distributions using maximally twisted mass fermions. We analyze two N_f=2+1+1 ensembles having pion masses of 210 MeV and 354 MeV at two values of the lattice spacing. The lattice scale is determined using the nucleon mass computed on a total of 18 N_f=2+1+1 ensembles generated at three values of the lattice spacing, $a$. The renormalization constants are evaluated non-perturbatively with a perturbative subtraction of ${\cal O}(a^2)$-terms. The moments of the generalized parton distributions are given in the $\bar{\rm MS}$ scheme at a scale of $ \mu=2$ GeV. We compare with recent results obtained using different discretization schemes. The implications on the spin content of the nucleon are also discussed.

Modeling nucleon generalized parton distributions

We discuss building models for nucleon generalized parton distributions (GPDs) H and E that are based on the formalism of double distributions (DDs). We found that the usual "DD+D-term" construction should be amended by an extra term, \xi E^1_+(x,\xi) built from the \alpha/\beta moment of the DD e(\beta,\alpha) that generates GPD E(x,\xi). Unlike the D-term, this function has support in the whole -1 \leq x \leq 1 region, and in general does not vanish at the border points |x|=\xi.

Nucleon Generalized Parton Distributions and Holographic Models

Using ideas from Light Front Holography, we discuss the calculation of the nucleon helicity-independent generalized parton distributions of quarks in the zero skewness case.

Moments of nucleon generalized parton distributions from lattice QCD

We present results on the lower moments of the nucleon generalized parton distri butions within lattice QCD using two dynamical flavors of degenerate twisted mass fermions. Our simulations are performed on lattices with three different values of the lattice spacings, namely $a=0.089$ fm, $a=0.070$ fm and $a=0.056$ fm, allowing the investigation of cut-off effects. The volume dependence is examined using simulations on two lattices of spatial length $L=2.1$ fm and $L=2.8$ fm. The simulations span pion masses in the range of 260-470 MeV. Our results are renormalized non-perturbatively and the values are given in the $\bar{\rm MS}$ scheme at a scale $ \mu=2$ GeV. They are chirally extrapolated to the physical point in order to compare with experiment. The consequences of these results on the spin carried by the quarks in the nucleon are investigated.

First moments of nucleon generalized parton distributions

We extrapolate the first moments of the generalized parton distributions using heavy baryon chiral perturbation theory. The calculation is based on the one loop level with the finite range regularization. The description of the lattice data is satisfactory and the extrapolated moments at physical pion mass are consistent with the results obtained with dimensional regularization, although the extrapolation in the momentum transfer to $t=0$ does show sensitivity to form factor effects which lie outside the realm of chiral perturbation theory. We discuss the significance of the results in the light of modern experiments as well as QCD inspired models.

Medium modifications of the bound nucleon generalized parton distributions and the quark contribution to the spin sum rule

We estimate the nuclear medium modifications of the quark contribution to the bound nucleon spin sum rule, ${J}^{{q}^{*}}$, as well the separate helicity, $\ensuremath{\Delta}{\ensuremath{\Sigma}}^{*}$, and the angular momentum, ${L}^{{q}^{*}}$, contributions to ${J}^{{q}^{*}}$. For the calculation of the bound nucleon generalized parton distributions (GPDs), we use as input the bound nucleon elastic form factors predicted in the quark-meson coupling model. Our model for the bound nucleon GPDs is relevant for incoherent deeply virtual Compton scattering (DVCS) with nuclear targets. We find that the medium modifications increase ${J}^{{q}^{*}}$ and ${L}^{{q}^{*}}$ and decrease $\ensuremath{\Delta}{\ensuremath{\Sigma}}^{*}$ compared to the free nucleon case. The effect is large and increases with increasing nuclear density \ensuremath{\rho}. For instance, at $\ensuremath{\rho}={\ensuremath{\rho}}_{0}=0.15 {\mathrm{fm}}^{\ensuremath{-}3},{J}^{{q}^{*}}$ increases by 7%, ${L}^{{q}^{*}}$ increases by 20%, and $\ensuremath{\Delta}{\ensuremath{\Sigma}}^{*}$ decreases by 17%. These in-medium modifications of the bound nucleon spin properties are a general feature of relativistic mean-field quark models and may be understood qualitatively in terms of the enhancement of the lower component of the quark Dirac spinor in the nuclear medium.

On the mistake in the implementation of the minimal model of the dual parametrization and resulting inability to describe the high-energy deeply virtual Compton data

We correct the mistaken claim made by Guzey and Polyakov [Eur. Phys. J. C 46, 151 (2006) ] and Guzey and Teckentrup [Phys. Rev. D 74, 054027 (2006)] that the minimal model of the dual parametrization of nucleon generalized parton distributions gives a good, essentially model-independent description of high-energy data on deeply virtual Compton scattering (DVCS). In the implementation of the dual parametrization by Guzey-Polyakov and Guzey-Teckentrup (see above), the numerical prefactor of two in front of the DVCS amplitude was missing. We show that the corrected minimal model of the dual parametrization significantly overestimates the Hadron Electron Ring Accelerator data (H1 and ZEUS experiments) on the DVCS cross section.

Chiral corrections of nucleon generalized parton distributions

Using heavy-baryon chiral perturbation theory (HBChPT), we study the leading chiral corrections to the complete set of nucleon generalized parton distributions (GPDs).